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This paper is concerned with a nonlinear wave equation which has been proposed as a model for conduit flow and migration of magma, namely A systematic search for conservation laws is performed, allowing all possible values of the two parameters n and m. In most cases, it is demonstrated that there exist precisely two independent laws and these are exhibited. However, two special cases m = 1, and m = n + 1, are discovered for which the proof is inconclusive and the second of these leads to a third law for a single parameter family.
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Shirley E. Harris (1996) studied this question.
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